One of the challenges of the modern photonics is to develop all‐optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested Parity‐Time (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non‐conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT‐symmetric photonic systems with an intensity‐dependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly‐induced PT‐symmetry breaking, and all‐optical switching. Nonlinear PT‐symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.
A Free-Lagrange numerical procedure for the
simulation of two-dimensional inviscid compressible flow
is described in detail. The
unsteady Euler equations are solved on an unstructured
Lagrangian grid based on a density-weighted Voronoi mesh.
The flow solver is of the Godunov type, utilising either the
HLLE (2 wave) approximate Riemann solver or the more recent HLLC
(3 wave) variant, each adapted to the Lagrangian frame.
Within each mesh cell, conserved properties are
treated as piece-wise linear, and a slope limiter of the MUSCL type
is used to
give non-oscillatory behaviour with nominal
second order accuracy in space.
The solver is first order accurate in time.
Modifications to the slope limiter to minimise
grid and coordinate dependent
effects are described.
The performances of the HLLE and HLLC solvers are compared for
two test problems; a one-dimensional
shock tube and a two-dimensional blast wave confined
within a rigid cylinder. The blast wave is initiated by impulsive
heating of a gas column whose centreline is parallel to,
and one half of the cylinder radius from,
the axis of the cylinder.
For the shock tube problem, both solvers predict shock and expansion
waves in good agreement with theory.
For the HLLE solver, contact resolution
is poor, especially in the blast wave problem. The HLLC solver achieves
near-exact contact capture in both problems.
Received May 25, 1995 / Accepted September 11, 1995 相似文献
Oblique indentation of power-law creeping solids by a rigid die is analysed in three dimensions with perfectly plastic behaviour emerging as an asymptotic case. Indenter profiles are prescribed to be axisymmetric for simplicity but not by necessity. Invariance and generality is aimed at, as the problem is governed by only four essential parameters, i.e. the die profile, p, the indentation angle, γ, the power-law exponent, n, and the coefficient of friction, μ. The solution strategy is based on a self-similar transformation resulting in a reduced problem corresponding to flat die indentation of complete contact. The reduced auxiliary problem, being independent of loading, history and time, was solved by a three-dimensional finite element analysis characterized by high accuracy. Subsequently, cumulative superposition was used to resolve the original problem and global and invariant relations between force, depth and contact area were determined. Detailed results are given for the location and shape of the contact region and stick/slip contours as well as for local states of surface stresses and deformation at flat and spherical indenters. Due to the asymmetry prevailing, it was found that in the spherical case, contact contours proved to be oval and shifted, although with normal and tangential forces only weakly coupled. Finite friction as compared to full adhesion proved to have only a minor effect on global relations. The framework laid down may be applied to the contact of structural assemblies subjected especially to elevated temperatures and also to various issues such as compaction of powder aggregates, flattening of rough surfaces and plastic impact. 相似文献
An experimental track layer tractor, based on an Allis Chalmers 8070 tractor (141 kW) was tested on bitumen covered concrete and on cultivated sandy loam at 7.8%; 13% and 21% soil water content. The two articulated beam-type tracks (500 mm wide × 2000 mm soil contact length) were constructed out of 500 mm long and 70 mm wide rubber covered steel track elements, carried by five steel cables (36 mm diameter). The tracks resisted inward deflection but allowed outward articulation between two smooth rear driving and two smooth front pneumatic truck tires (1060 mm diameter) per track. The contact pressure and the tangential force on an instrumented track element, as well as the total torque input to one track, were simultaneously recorded during the drawbar pull/slip tests.
Different possible pressure distribution profiles under the tracks were considered and compared to the recorded data. Two possible traction models are proposed, one constant pressure model for minimal inward track deflection, and a deformable track model with inward deflection and a higher contact pressure at both the front free-wheeling and rear driving tires. For both models, the traction force was generated mainly by rubber/soil friction and adhesion and limited soil shear. A close agreement between the measured and predicted contact pressures and traction force for individual track elements, based on the deformable track model, was observed. The recorded and calculated coefficient of traction based on the summation of the force for the series of track elements were comparable, but were considerably lower than the predicted values, probably due to internal track friction rather than soil sinkage. The tractive efficiency for both a hard or soft surface was also unacceptably low, probably caused by internal track friction. 相似文献
An exact analytical solution is found to a nonlinear boundary-value deformation problem for a long noncircular cylindrical
shell of variable curvature. The shell is subject to bending moments at the edges. The dependence of the stress-strain state
of the shell on the curvature is analyzed
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 93–100, November 2006. 相似文献